%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ARI586_1 : TPTP v9.3.1. Released v5.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 09:33:25 AM UTC 2026
% Result : Theorem 2.79s 1.16s
% Output : Refutation 2.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 21 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 35 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 13 ~; 5 |; 4 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number arithmetic : 72 ( 25 atm; 14 fun; 18 num; 15 var)
% Number of types : 1 ( 0 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 2 usr; 5 con; 0-2 aty)
% Number of variables : 15 ( 12 !; 3 ?; 15 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_6,type,
sK0: $int ).
tff(func_def_7,type,
sF1: $int ).
tff(f1,conjecture,
! [X0: $int] :
( $less(0,X0)
=> ? [X1: $int] :
( $less(X0,X1)
& $less(X1,$product(X0,3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_Y_between_X_and_3X) ).
tff(f2,negated_conjecture,
~ ! [X0: $int] :
( $less(0,X0)
=> ? [X1: $int] :
( $less(X0,X1)
& $less(X1,$product(X0,3)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
! [X0: $int,X1: $int] : ( $sum(X1,X0) = $sum(X0,X1) ),
introduced(definition,[],[tha_commutativity]) ).
tff(f8,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(definition,[],[tha_non-reflexivity]) ).
tff(f12,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(definition,[],[tha_order_plus_one_dichotomy]) ).
tff(f21,plain,
? [X0: $int] :
( ! [X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$product(X0,3)) )
& $less(0,X0) ),
inference(ennf_transformation,[],[f2]) ).
tff(f22,plain,
( ! [X1: $int] :
( ~ $less(sK0,X1)
| ~ $less(X1,$product(sK0,3)) )
& $less(0,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f21]) ).
tff(f23,plain,
$less(0,sK0),
inference(cnf_transformation,[],[f22]) ).
tff(f24,plain,
! [X1: $int] :
( ~ $less(sK0,X1)
| ~ $less(X1,$product(sK0,3)) ),
inference(cnf_transformation,[],[f22]) ).
tff(f26,definition,
sF1 = $product(sK0,3),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
tff(f27,plain,
! [X1: $int] :
( ~ $less(sK0,X1)
| ~ $less(X1,sF1) ),
inference(definition_folding,[],[f24,f26]) ).
tff(f29,definition,
( spl2_1
<=> ( sF1 = $product(sK0,3) ) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f32,plain,
spl2_1,
inference(avatar_split_clause,[],[f26,f29]) ).
tff(f34,definition,
( spl2_2
<=> $less(0,sK0) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f37,plain,
spl2_2,
inference(avatar_split_clause,[],[f23,f34]) ).
tff(f59,plain,
! [X0: $int] : $less(X0,$sum(X0,1)),
inference(resolution,[],[f12,f8]) ).
tff(f239,plain,
~ $less($sum(sK0,1),sF1),
inference(resolution,[],[f59,f27]) ).
tff(f244,plain,
~ $less($sum(1,sK0),sF1),
inference(forward_demodulation,[],[f239,f3]) ).
tff(f246,definition,
( spl2_6
<=> $less($sum(1,sK0),sF1) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f249,plain,
~ spl2_6,
inference(avatar_split_clause,[],[f244,f246]) ).
tff(f250,plain,
$false,
inference(avatar_smt_refutation,[],[f249,f37,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ARI586_1 : TPTP v9.3.1. Released v5.1.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n026.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 20:55:42 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.79/1.16 % (58460)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 2.79/1.16 % (58471)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1064967090:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 2.79/1.16 % (58471)First to succeed.
% 2.79/1.16 % (58471)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-58460"
% 2.79/1.16 % (58465)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3425692896:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 2.79/1.16 % (58470)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=603819564:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 2.79/1.16 % (58467)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=3493896814:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 2.79/1.16 % (58469)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=1160715606:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 2.79/1.16 % (58468)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=424292634:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 2.79/1.16 % (58466)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=501251495:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 2.79/1.16 % (58469)Instruction limit reached!
% 2.79/1.16 % (58469)------------------------------
% 2.79/1.16 % (58469)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58469)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58469)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58469)Termination reason: Instruction limit
% 2.79/1.16 % (58469)Termination phase: Saturation
% 2.79/1.16 % (58469)Time elapsed: 0.004 s
% 2.79/1.16 % (58469)Peak memory usage: 88 MB
% 2.79/1.16 % (58469)Instructions burned: 4 (million)
% 2.79/1.16 % (58468)Instruction limit reached!
% 2.79/1.16 % (58468)------------------------------
% 2.79/1.16 % (58468)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58468)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58468)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58468)Termination reason: Instruction limit
% 2.79/1.16 % (58468)Termination phase: Saturation
% 2.79/1.16 % (58468)Time elapsed: 0.006 s
% 2.79/1.16 % (58468)Peak memory usage: 88 MB
% 2.79/1.16 % (58468)Instructions burned: 8 (million)
% 2.79/1.16 % (58470)Refutation not found, incomplete strategy
% 2.79/1.16 % (58470)------------------------------
% 2.79/1.16 % (58470)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58470)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58470)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58470)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.16 % (58470)Time elapsed: 0.029 s
% 2.79/1.16 % (58470)Peak memory usage: 114 MB
% 2.79/1.16 % (58470)Instructions burned: 6 (million)
% 2.79/1.16 % (58466)Refutation not found, incomplete strategy
% 2.79/1.16 % (58466)------------------------------
% 2.79/1.16 % (58466)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58466)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58466)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58466)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.16 % (58466)Time elapsed: 0.029 s
% 2.79/1.16 % (58466)Peak memory usage: 115 MB
% 2.79/1.16 % (58466)Instructions burned: 6 (million)
% 2.79/1.16 % (58465)Also succeeded, but the first one will report.
% 2.79/1.16 % (58479)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1278639520:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 2.79/1.16 % (58467)Instruction limit reached!
% 2.79/1.16 % (58467)------------------------------
% 2.79/1.16 % (58467)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58467)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58467)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58467)Termination reason: Instruction limit
% 2.79/1.16 % (58467)Termination phase: Saturation
% 2.79/1.16 % (58467)Time elapsed: 0.137 s
% 2.79/1.16 % (58467)Peak memory usage: 117 MB
% 2.79/1.16 % (58467)Instructions burned: 201 (million)
% 2.79/1.16 % (58479)Refutation not found, incomplete strategy
% 2.79/1.16 % (58479)------------------------------
% 2.79/1.16 % (58479)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58479)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58479)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58479)Termination reason: Refutation not found, incomplete strategy
% 2.79/1.16 % (58479)Time elapsed: 0.001 s
% 2.79/1.16 % (58479)Peak memory usage: 88 MB
% 2.79/1.16 % (58471)Refutation found. Thanks to Tanya!
% 2.79/1.16 % SZS status Theorem for theBenchmark
% 2.79/1.16 % SZS output start Proof for theBenchmark
% See solution above
% 2.79/1.16 % (58471)------------------------------
% 2.79/1.16 % (58471)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.79/1.16 % (58471)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.79/1.16 % (58471)CaDiCaL version: 2.1.3
% 2.79/1.16 % (58471)Termination reason: Refutation
% 2.79/1.16 % (58471)Time elapsed: 0.025 s
% 2.79/1.16 % (58471)Peak memory usage: 116 MB
% 2.79/1.16 % (58471)Instructions burned: 20 (million)
% 2.79/1.16 % (58471)------------------------------
% 2.79/1.16 % (58471)------------------------------
% 2.79/1.16 % (58460)Success in time 0.303 s
% 2.79/1.16 % Vampire exiting
%------------------------------------------------------------------------------